Differential equation-based minimal model describing metabolic oscillations in
            <i>Bacillus subtilis</i>
            biofilms

Garde, Ravindra; Ibrahim, Bashar; Kovács, Ákos T.; Schuster, Stefan

doi:10.1098/rsos.190810

Cited by 10 publications

(14 citation statements)

References 48 publications

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“…Simulating either of these model variants leads to results that do not show qualitative differences from the three-variable version 11 , except that the oscillations are more spike-like ( Fig. 2a).…”

Section: Resultsmentioning

confidence: 95%

“…This formally implies that Table 1. (b) Bifurcation diagrams of G p versus G E for the c6ODE model and (inset) BM 11 . The supercritical Hopf bifurcation occurs at G E = 28 mmol/l in the c6ODE (for BM bifurcation at G E = 24.4 mmol/l) but qualitatively, the model has not changed.…”

Section: Michaelis-menten Kinetics Along With Reversible Reactionsmentioning

confidence: 99%

“…We did this by employing a previously known minimal oscillator involving three ODEs, proposed by Wilhelm and Heinrich, aimed to describe chemical reactions 12 . The three ODEs in variables X, Y, and Z in the minimal oscillator corresponded, in our adapted model, to glutamate in the periphery (G p ), interior (G i ) and ammonia (A) respectively and were found to adequately describe the biofilm oscillations 11 . The system of equations of the basic model (BM) is as follows:…”

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confidence: 95%

“…and glutamate, and two more ODEs describe the dynamics of housekeeping proteins and the enzyme glutamate dehydrogenase (GDH). In our approach, we focus solely on the two metabolites: glutamate and ammonia, and thus describe the same process in a minimal model 11 . We did this by employing a previously known minimal oscillator involving three ODEs, proposed by Wilhelm and Heinrich, aimed to describe chemical reactions 12 .…”

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confidence: 99%

“…Interior cells produce ammonia using glutamate (rate k 5 G i ) since that produced by the periphery is lost to the environment and is a waste of nitrogen. Peripheral cells use the ammonia diffusing out from the interior in addition to the glutamate supplied in the microfluidics chamber to produce biomass (k 2 AG p ) 11 . However, the loss of ammonia due to diffusion to the environment (k 3 A) is much greater than its consumption to produce biomass; hence the term k 2 AG p is neglected in equation BM2.…”

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confidence: 99%

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Extending the minimal model of metabolic oscillations in Bacillus subtilis biofilms

Garde

Ibrahim

Schuster

2020

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Biofilms are composed of microorganisms attached to a solid surface or floating on top of a liquid surface. They pose challenges in the field of medicine but can also have useful applications in industry. Regulation of biofilm growth is complex and still largely elusive. Oscillations are thought to be advantageous for biofilms to cope with nutrient starvation and chemical attacks. Recently, a minimal mathematical model has been employed to describe the oscillations in Bacillus subtilis biofilms. In this paper, we investigate four different modifications to that minimal model in order to better understand the oscillations in biofilms. Our first modification is towards making a gradient of metabolites from the center of the biofilm to the periphery. We find that it does not improve the model and is therefore, unnecessary. We then use realistic Michaelis-Menten kinetics to replace the highly simple massaction kinetics for one of the reactions. Further, we use reversible reactions to mimic the diffusion in biofilms. As the final modification, we check the combined effect of using Michaelis-Menten kinetics and reversible reactions on the model behavior. We find that these two modifications alone or in combination improve the description of the biological scenario. Biofilms, a complex aggregation of cells embedded in a polysaccharide matrix, have been of interest for a long time in history-right when Antoine van Leuwenhoek examined a scraping of his tooth plaqueunder a microscope that he had built 1. Since then, our understanding of biofilms has greatly broadened. We now know that living as a close aggregation provides several advantages to bacteria, such as the efficient distribution of macronutrients, removal of waste products, defense from chemical stress, and better gaseous exchange in the case of pellicle biofilms on the surface of liquids 2,3. Biofilms are an elaborate system of coexisting individual cells that exhibit several social dynamics, including the division of labour 4-7. In experiments using a microfluidics chamber, oscillations were observed in the growth of Bacillus subtilis 4 which was supplied with glutamate on one end of the chamber while the waste products of the biofilm were washed off at the other end at a constant rate. The peripheral cells of the biofilm have the advantage of direct access to glutamate. On the downside, they lose small molecules like ammonia which is an important source of nitrogen 8. Cells in the interior, on the other hand, depend on the leftover glutamate that diffuses inwards in the biofilm, but do not lose gaseous molecules as rapidly as the peripheral cells. Thus cells in different regions of the biofilm will likely exhibit differences in their metabolic behavior 7. The interior cells produce ammonia, which is required to produce glutamine. Glutamine is a proxy for the protein content and thus for the growth of the biofilm 9. The peripheral cells depend on the ammonia diffusing from the interior for their growth. Thus, interior cells control the growth of the peripheral ...

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Section: Resultsmentioning

confidence: 95%

Section: Michaelis-menten Kinetics Along With Reversible Reactionsmentioning

confidence: 99%

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confidence: 95%

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confidence: 99%

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confidence: 99%

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